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Answer :
To find the product of the binomials [tex](5x - 4)(7x - 9)[/tex], we'll use the distributive property, also known as the FOIL method (First, Outside, Inside, Last). This method helps in multiplying each term in the first binomial with each term in the second binomial. Let's break it down step-by-step.
First: Multiply the first terms in each binomial:
[tex]5x \times 7x = 35x^2[/tex]Outside: Multiply the outer terms in the product:
[tex]5x \times (-9) = -45x[/tex]Inside: Multiply the inner terms in the product:
[tex](-4) \times 7x = -28x[/tex]Last: Multiply the last terms in each binomial:
[tex](-4) \times (-9) = 36[/tex]
Now, combine all these results to form the expanded expression:
[tex]35x^2 - 45x - 28x + 36[/tex]
Finally, combine the like terms, which are the [tex]x[/tex] terms:
[tex]35x^2 - 73x + 36[/tex]
The correct answer is then Option D: [tex]35x^2 - 73x + 36[/tex].
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